Is the sum of 3 primes problem solved?...

Asked by:

HI MaplePrimes,

Is the Goldbach Weak Conjecture proven?

Consider odd primes p, q, and r.  The question is, Is the sum p+q+r sufficient to reach all odd numbers greater than 9?

See -

https://en.wikipedia.org/wiki/Goldbach's_weak_conjecture

I tried an example.

looping_for_Goldbach_Weak_Conjecture_8.mw

looping_for_Goldbach_Weak_Conjecture_8.pdf

Regards,

Matt

Matt's first exploration of Leyland numbers 10-28-...

Asked by:

Hi everybody,

So today is 10-28-2016 and I explored Leyland Numbers for the first time, on Maple.  Please see my example file and let me know what your impression is.

x_to_the_yth_power_and_y_to_the_xth_power_take_4.mw

x_to_the_yth_power_and_y_to_the_xth_power_take_4.pdf

I have included a .pdf file so that the caual internet observer can also be aware of this information.

Regards,
Matt

How to compute an extension of finite field?...

Asked by:

Hi EveryOne!

In the answer of the question "How to find roót of polynomial in finite field and extension finite field ", @Carl Love helped me to find roots of polynimial in finite field and extension finite field (At URL http://www.mapleprimes.com/view.aspx?sf=215097_Answer/Primfield.mw OR http://www.mapleprimes.com/view.aspx?sf=215285_Answer/Matrix_powers_finite_field.mw)

However, with matrix M: =< x^4+x^3+x^6+x^7+x, 1+x^2+x^4+x^5+x^6, 1+x+x^2+x^3, x^7+x^6+x^5+x^4;

x^7+x^5+x^4+x^3, x^6+x^4+x^2+1, x^4+x^3+x^6+x^7+x^2+x+1, 1+x^2+x^3+x^4+x^5;

x^7+x^5+x^2, x^7+x^5+x^3+x^2+1, x^2+x+x^6, x^2+x^3+x^5;
x^4+x^3+x^6+1, 1+x^2+x^3+x^4, x^6+x^5+x^4+x^3, x^7+x^3 >;

and GF(2^8)/f(x)=x^8 + x^7 +x^6 + x +1 (i.e ext1:= Z^8+Z^7+Z^6+Z+1), then program Primfield.mw don't run!

Please help me! Thanks so much.

Maple special_primes...

Asked by:

I am trying to understand how maple "isprime" algorithm works. But I can't find anywhere what special_primes means.

showstat(isprime);

isprime := proc(n)
local btor, nr, p, r;
1   if not type(n,'integer') then
2     if type(n,('complex')('numeric')) then
3       error "argument must be an integer"
else
4       return 'isprime(n)'
end if
end if;
5   if n < 2 then
6     return false
elif member(n,isprime:-special_primes) then
7     return true
elif igcd(2305567963945518424753102147331756070,n) <> 1 then
8     return false
elif n < 10201 then
9     return true
elif igcd(8496969489233418110532339909187349965926062586648932736611545426342203893270769390909069477309509137509786917118668028861499333825097682386722983737962963066757674131126736578936440788157186969893730633113066478620448624949257324022627395437363639038752608166758661255956834630697220447512298848222228550062683786342519960225996301315945644470064720696621750477244528915927867113,n) <> 1 then
10     return false
elif n < 1018081 then
11     return true
else
12     r := gmp_isprime(n);
13     if not r or n <= 5000000000 then
14       return r
end if;
15     nr := igcd(408410100000,n-1);
16     nr := igcd(nr^5,n-1);
17     r := iquo(n-1,nr);
18     btor := modp(('power')(2,r),n);
19     if cyclotest(n,btor,2,r) = false or irem(nr,3) = 0 and cyclotest(n,btor,3,r) = false or irem(nr,5) = 0 and cyclotest(n,btor,5,r) = false or irem(nr,7) = 0 and cyclotest(n,btor,7,r) = false then
20       return false
end if;
21     if isqrt(n)^2 = n then
22       return false
end if;
23     for p from 3 while numtheory:-jacobi(p^2-4,n) <> -1 do
24       NULL
end do;
25     return evalb(TraceModQF(p,n+1,n) = [2, p])
end if
end proc

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